MonteCarloAverage {lgcp}

MonteCarloAverage function

Description

This function creates an object of class MonteCarloAverage. The purpose of the function is to compute Monte Carlo expectations online in the function lgcpPredict, it is set in the argument gridmeans of the argument output.control.

Usage

MonteCarloAverage(funlist, lastonly = TRUE)

Arguments

funlist

a character vector of names of functions, each accepting single argument Y

lastonly

compute average using only time T? (see ?lgcpPredict for definition of T)

Details

A Monte Carlo Average is computed as:

E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_1:t_2})] \approx \frac1n\sum_{i=1}^n g(Y_{t_1:t_2}^{(i)})

where g is a function of interest, Y_{t_1:t_2}^{(i)} is the ith retained sample from the target and n is the total number of retained iterations. For example, to compute the mean of Y_{t_1:t_2} set,

g(Y_{t_1:t_2}) = Y_{t_1:t_2},

the output from such a Monte Carlo average would be a set of t_2-t_1 grids, each cell of which being equal to the mean over all retained iterations of the algorithm (NOTE: this is just an example computation, in practice, there is no need to compute the mean on line explicitly, as this is already done by defaul in lgcpPredict). For further examples, see below. The option last=TRUE computes,

E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_2})],

so in this case the expectation over the last time point only is computed. This can save computation time.

Value

object of class MonteCarloAverage

See Also

setoutput, lgcpPredict, GAinitialise, GAupdate, GAfinalise, GAreturnvalue, exceedProbs

Examples

fun1 <- function(x){return(x)}   # gives the mean
fun2 <- function(x){return(x^2)} # computes E(X^2). Can be used with the 
                                 # mean to compute variances, since 
                                 # Var(X) = E(X^2) - E(X)^2
fun3 <- exceedProbs(c(1.5,2,3))  # exceedance probabilities, 
                                 #see ?exceedProbs
mca <- MonteCarloAverage(c("fun1","fun2","fun3"))
mca2 <- MonteCarloAverage(c("fun1","fun2","fun3"),lastonly=TRUE)